I and my opponent play a game of dices. I win if my opponent didn't throw a dice in our game with a higher number than my highest number.
Example : I have 2 dices, he's got 3 . Our throws : (1,4,2,4,3) , I threw 1,4 he 2,3,4. I won in this case because he didn't get any higher number than my 4. (he should've gotten a 5 or 6) The dices are also distinguishable.
Give the number of possible combinations in which I can win if:
1) I have 2 dices, he's got 1.
2) I have 3 dices and my opponent 2.
My incomplete solution:(let $i$ be my throws and $o$ for opponent)
1) (i1, i2, o1) here are possible $6^3$ total combinations .
$wins=6^3 - |o1>max(i1,i2)|$ (but I don't know how to count it)
2) no idea